75 citations · 211 across the 27 of their papers we have counts for
33 papers
Variational Seasonal-Trend Decomposition with Sparse Continuous-Domain Regularization
Julien Fageot
We consider the inverse problem of recovering a continuous-domain function from a finite number of noisy linear measurements. The unknown signal is modeled as the sum of a slowly v…
Generalized Bradley-Terry Models for Score Estimation from Paired Comparisons
Julien Fageot, Sadegh Farhadkhani, Lê Nguyên Hoang +1
Many applications, e.g. in content recommendation, sports, or recruitment, leverage the comparisons of alternatives to score those alternatives. The classical Bradley-Terry model a…
Complex-Order Scale-Invariant Operators and Self-Similar Processes
Arash Amini, Julien Fageot, Michael Unser
Derivatives and integration operators are well-studied examples of linear operators that commute with scaling up to a fixed multiplicative factor; i.e., they are scale-invariant. F…
TV-based Spline Reconstruction with Fourier Measurements: Uniqueness and Convergence of Grid-Based Methods
Thomas Debarre, Quentin Denoyelle, Julien Fageot
We study the problem of recovering piecewise-polynomial periodic functions from their low-frequency information. This means that we only have access to possibly corrupted versions…
On Tempered Discrete and Lévy White Noises
Julien Fageot
We study the growth properties of the family of i.i.d. random sequences, also known as discrete white noises, and of their continuous-domain generalization, the family of Lévy whit…
Functional Estimation of Anisotropic Covariance and Autocovariance Operators on the Sphere
Alessia Caponera, Julien Fageot, Matthieu Simeoni +1
We propose nonparametric estimators for the second-order central moments of possibly anisotropic spherical random fields, within a functional data analysis context. We consider a m…
A Fast and Scalable Polyatomic Frank-Wolfe Algorithm for the LASSO
Adrian Jarret, Julien Fageot, Matthieu Simeoni
We propose a fast and scalable Polyatomic Frank-Wolfe (P-FW) algorithm for the resolution of high-dimensional LASSO regression problems. The latter improves upon traditional Frank-…
The Critical Smoothness of Generalized Functions
Julien Fageot, John Paul Ward
For each integrability parameter , the critical smoothness of a periodic generalized function , denoted by is the supremum over the smoothness paramet…
On the Uniqueness of Solutions for the Basis Pursuit in the Continuum
Thomas Debarre, Quentin Denoyelle, Julien Fageot
This paper studies the continuous-domain inverse problem of recovering Radon measures on the one-dimensional torus from low-frequency Fourier coefficients, where Kc is the cutoff f…
Entropic Compressibility of Lévy Processes
Julien Fageot, Alireza Fallah, Thibaut Horel
In contrast to their seemingly simple and shared structure of independence and stationarity, Lévy processes exhibit a wide variety of behaviors, from the self-similar Wiener proces…
TV-based Reconstruction of Periodic Functions
Julien Fageot, Matthieu Simeoni
We introduce a general framework for the reconstruction of periodic multivariate functions from finitely many and possibly noisy linear measurements. The reconstruction task is for…
3D Solid Spherical Bispectrum CNNs for Biomedical Texture Analysis
Valentin Oreiller, Vincent Andrearczyk, Julien Fageot +2
Locally Rotation Invariant (LRI) operators have shown great potential in biomedical texture analysis where patterns appear at random positions and orientations. LRI operators can b…
Local Rotation Invariance in 3D CNNs
Vincent Andrearczyk, Julien Fageot, Valentin Oreiller +2
Locally Rotation Invariant (LRI) image analysis was shown to be fundamental in many applications and in particular in medical imaging where local structures of tissues occur at arb…
Wavelet Compressibility of Compound Poisson Processes
Shayan Aziznejad, Julien Fageot
In this paper, we precisely quantify the wavelet compressibility of compound Poisson processes. To that end, we expand the given random process over the Haar wavelet basis and we a…
Sparsest Piecewise-Linear Regression of One-Dimensional Data
Thomas Debarre, Quentin Denoyelle, Michael Unser +1
We study the problem of one-dimensional regression of data points with total-variation (TV) regularization (in the sense of measures) on the second derivative, which is known to pr…
Native Banach spaces for splines and variational inverse problems
Michael Unser, Julien Fageot
We propose a systematic construction of native Banach spaces for general spline-admissible operators . In short, the native space for and the (dual) norm $\|\cdo…
Dictionary Learning for Two-Dimensional Kendall Shapes
Anna Song, Virginie Uhlmann, Julien Fageot +1
We propose a novel sparse dictionary learning method for planar shapes in the sense of Kendall, namely configurations of landmarks in the plane considered up to similitudes. Our sh…
Support and Approximation Properties of Hermite Splines
Julien Fageot, Shayan Aziznejad, Michael Unser +1
In this paper, we formally investigate two mathematical aspects of Hermite splines which translate to features that are relevant to their practical applications. We first demonstra…
Principled Design and Implementation of Steerable Detectors
Julien Fageot, Virginie Uhlmann, Zsuzsanna Püspöki +3
We provide a complete pipeline for the detection of patterns of interest in an image. In our approach, the patterns are assumed to be adequately modeled by a known template, and ar…
Periodic Splines and Gaussian Processes for the Resolution of Linear Inverse Problems
Anaïs Badoual, Julien Fageot, Michael Unser
This paper deals with the resolution of inverse problems in a periodic setting or, in other terms, the reconstruction of periodic continuous-domain signals from their noisy measure…
Continuous-Domain Solutions of Linear Inverse Problems with Tikhonov vs. Generalized TV Regularization
Harshit Gupta, Julien Fageot, Michael Unser
We consider linear inverse problems that are formulated in the continuous domain. The object of recovery is a function that is assumed to minimize a convex objective functional. Th…
Wavelet Analysis of the Besov Regularity of Lévy White Noises
Shayan Aziznejad, Julien Fageot
We characterize the local smoothness and the asymptotic growth rate of the Lévy white noise. We do so by characterizing the weighted Besov spaces in which it is located. We extend…
Beyond Wiener's Lemma: Nuclear Convolution Algebras and the Inversion of Digital Filters
Julien Fageot, Michael Unser, John Paul Ward
A convolution algebra is a topological vector space that is closed under the convolution operation. It is said to be inverse-closed if each element of w…
Angular Accuracy of Steerable Feature Detectors
Zsuzsanna Püspöki, Arash Amini, Julien Fageot +2
The detection of landmarks or patterns is of interest for extracting features in biological images. Hence, algorithms for finding these keypoints have been extensively investigated…